Question

if P is a prime number and P divides k3 then p divides
​

Answer 1

Answer:

then p divides the 3

Step-by-step explanation:

if p

divides k3 then p divides 3

Answer 2

Answer:

p also divides k.

Step-by-step explanation:

Let us say prime factorisation of k³ is

k³= pⁿ × q

where n is a natural number and q is the product of other prime factors.

Then,

∛k³=∛(pⁿ×q)

⇒k=p^n/3 * ∛q

It is clear that we have not proved that n/3 is a natural number.

But if k is not divisible by p, k³ cannot be divisible by p since k³=k*k*k.

Hence proved.

Hope it helps!

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